$\mu$-model for the statics of dry granular medium

TL;DR

This paper introduces a new framework for modeling dry granular media using a distribution of friction coefficients, deriving key parameters like the Janssen coefficient, and analyzing pressure distribution behaviors.

Contribution

It presents a novel approach based on friction coefficient distributions and provides analytical solutions for the silo problem and pressure maxima in granular media.

Findings

Derived the Janssen coefficient dependence on friction coefficients.

Identified conditions for maximum pressure distribution with depth.

Proposed a general framework using a dry friction tensor for granular media.

Abstract

We propose the description of the granular matter which is based on distribution of dry friction coefficients. Using such a concept and a simple one-dimensional packing of grains we solve the silo problem. The friction coefficients at contacts are determined both by geometry of packing configuration and the stress distribution in a medium. Within such an approach the Janssen coefficient is determined and its dependence on the particle-particle and boundary-particle friction coefficients is obtained. Also we investigate the conditions for the appearance of the maximum in the pressure distribution with the depth with overweight on top. As an outcome of our work we propose the general framework to the description of the granular matter as a continual medium which is characterized by the field of the dry friction tensor.